Influence of noise on generalized synchronization in systems with a complex topology of attractor

Abstract

Background and Objectives: The goal of the paper is to study the influence of noise on generalized synchronization in unidirectionally coupled systems with a complex topology of attractor. As the systems under study, two models of chaotic systems with two-sheeted topologies of attractors such as Lorenz and Chen systems are considered. Materials and Methods: For the synchronous regime detection the method of calculating the spectrum of Lyapunov exponents for coupled systems and the auxiliary system approach are used. Results: It has been shown that the dependences of the threshold for the onset of the generalized synchronization regime on the noise intensity do not practically change both for Lorenz and Chen systems. Conclusion: Using the examples of Lorenz oscillators and Chen systems we have found that the generalized synchronization regime in systems with a complex topology of attractor is stable to external noise. This behavior of systems is determined by the weak influence of noise on the structure of attractors of interacting systems, which is confirmed by constructing their phase portraits for different values of the noise intensity

Keywords

• generalized synchronization
• auxiliary system approach
• calculation of the spectrum of lyapunov exponents
• noise
• complex topology of attractor